| EPSRC Reference: |
GR/M90108/01 |
| Title: |
NONLINEAR STABILITY OF FLUID FLOWS IN ASYMMETRIC DOMAINS |
| Principal Investigator: |
Vanneste, Professor J |
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| Department: |
Sch of Mathematics |
| Organisation: |
University of Edinburgh |
| Scheme: |
Standard Research (Pre-FEC) |
| Starts: |
01 January 2000 |
Ends: |
31 December 2001 |
Value (£): |
50,423
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| EPSRC Research Topic Classifications: |
| Continuum Mechanics |
Fluid Dynamics |
| Non-linear Systems Mathematics |
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| EPSRC Industrial Sector Classifications: |
| No relevance to Underpinning Sectors |
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Summary on Grant Application Form |
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Non-linear stability conditions have been derived for a wide range of two-dimensional and quasi geostrophic fluid flows using Arnold's energy-Casimir-momentum method. However, in many cases, the method relies on the symmetry properties of the fluid domain: when the domain has no continuous symmetries, as is the case for realistic flows, the method becomes ineffective. This raises the following question which motivates this project: how are the qualitative conclusions on stability in symmetric domains modified in (slightly) asymmetric domains?To investigate this question, we will (i) establish the conditions under which steady flows persist under perturbations of the domain shape; (ii) derive non-linear stability conditions for the flows which persist by extending Arnold's method: (iii) study linear and non-linear mechanisms that may be responsible for the destabilisation of certain flows; and (iv) derive saturation bounds for unstable flows in order to assess the physical importance of the instabilities. Analytical work using perturbation methods and (Hamiltonian) dynamical-system techniques will be complemented by numerical simulations of fluid flows. Particular attention will be paid to the case of a slightly deformed spherical domain, in view of the implications of the results for the dynamics of large-scale structures in terrestrial and planetary atmospheres.
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Key Findings |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Potential use in non-academic contexts |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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Impacts |
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| Description |
This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk |
| Summary |
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| Date Materialised |
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Sectors submitted by the Researcher |
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This information can now be found on Gateway to Research (GtR) http://gtr.rcuk.ac.uk
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| Project URL: |
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| Further Information: |
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| Organisation Website: |
http://www.ed.ac.uk |